Susceptible-exposed-infectious-recovered Research Articles

Managing two-dose COVID-19 vaccine rollouts with limited supply: Operations strategies for distributing time-sensitive resources.

Distributing scarce resources such as COVID‐19 vaccines is often a highly time‐sensitive and mission‐critical operation. Our research was prompted by a significant obstacle that the United States and other nations encountered during the early months of the COVID‐19 vaccination campaign: Most COVID‐19 vaccines require two doses given 3 or 4 weeks apart. Given the severely limited supply and mounting pressure on many countries to reduce hospitalizations and mortality, how to effectively roll out two‐dose vaccines was a critical policy decision. In this paper, we first model and analyze inventory dynamics of the rollout process under three rollout strategies: (1) holding back second doses, (2) releasing second doses, and (3) stretching the lead time between doses. Then we develop an SEIR (susceptible, exposed, infectious, recovered) model that incorporates COVID‐19 asymptomatic and symptomatic infections to evaluate these strategies in terms of infections, hospitalizations, and mortality. Among our findings, we show releasing second doses reduces infections but creates uneven vaccination patterns. In addition, to ensure second doses are given on time without holding back inventory, strictly less than half of the supply can be allocated to first‐dose appointments. Stretching the between‐dose lead time flattens the infection curve and reduces both hospitalizations and mortality compared with the strategy of releasing second doses. We also consider an alternative single‐dose vaccine with lower efficacy and show that the vaccine can be more effective than its two‐dose counterparts in reducing infections and mortality. We conduct extensive sensitivity analyses related to age composition, risk‐based prioritization, supply disruptions, and disease transmissibility. Our paper provides important implications for policymakers to develop effective vaccine rollout strategies in developed and developing countries alike. More broadly, our paper sheds light on how to develop effective operations strategies for distributing time‐sensitive resources in times of crisis.

Modeling vaccination and control strategies for outbreaks of monkeypox at gatherings.

The monkeypox outbreak in non-endemic countries in recent months has led the World Health Organization (WHO) to declare a public health emergency of international concern (PHEIC). It is thought that festivals, parties, and other gatherings may have contributed to the outbreak. We considered a hypothetical metropolitan city and modeled the transmission of the monkeypox virus in humans in a high-risk group (HRG) and a low-risk group (LRG) using a Susceptible-Exposed-Infectious-Recovered (SEIR) model and incorporated gathering events. Model simulations assessed how the vaccination strategies combined with other public health measures can contribute to mitigating or halting outbreaks from mass gathering events. The risk of a monkeypox outbreak was high when mass gathering events occurred in the absence of public health control measures. However, the outbreaks were controlled by isolating cases and vaccinating their close contacts. Furthermore, contact tracing, vaccinating, and isolating close contacts, if they can be implemented, were more effective for the containment of monkeypox transmission during summer gatherings than a broad vaccination campaign among HRG, when accounting for the low vaccination coverage in the overall population, and the time needed for the development of the immune responses. Reducing the number of attendees and effective contacts during the gathering could also prevent a burgeoning outbreak, as could restricting attendance through vaccination requirements. Monkeypox outbreaks following mass gatherings can be made less likely with some restrictions on either the number and density of attendees in the gathering or vaccination requirements. The ring vaccination strategy inoculating close contacts of confirmed cases may not be enough to prevent potential outbreaks; however, mass gatherings can be rendered less risky if that strategy is combined with public health measures, including identifying and isolating cases and contact tracing. Compliance with the community and promotion of awareness are also indispensable to containing the outbreak.

A swarm-optimizer-assisted simulation and prediction model for emerging infectious diseases based on SEIR

Mechanism-driven models based on transmission dynamics and statistic models driven by public health data are two main methods for simulating and predicting emerging infectious diseases. In this paper, we intend to combine these two methods to develop a more comprehensive model for the simulation and prediction of emerging infectious diseases. First, we combine a standard epidemic dynamic, the susceptible–exposed–infected–recovered (SEIR) model with population migration. This model can provide a biological spread process for emerging infectious diseases. Second, to determine suitable parameters for the model, we propose a data-driven approach, in which the public health data and population migration data are assembled. Moreover, an objective function is defined to minimize the error based on these data. Third, based on the proposed model, we further develop a swarm-optimizer-assisted simulation and prediction method, which contains two modules. In the first module, we use a level-based learning swarm optimizer to optimize the parameters required in the epidemic mechanism. In the second module, the optimized parameters are used to predicate the spread of emerging infectious diseases. Finally, various experiments are conducted to validate the effectiveness of the proposed model and method.

Complex dynamics and control strategies of SEIR heterogeneous network model with saturated treatment

In this paper, we introduce saturated treatment into the network-based Susceptible–Exposed–Infected–Recovered (SEIR) epidemic model. By the stability analysis of disease-free equilibrium, we notice that unlike the common situation, the basic reproduction number R0<1 cannot guarantee the global stability of disease-free equilibrium, which indicates that the stronger condition of R0<R̂0<1 is required. We then investigate the bifurcation behavior of the model under different saturated treatment coefficient α. When the medical resources are limited (i.e., large α) a backward bifurcation occurs such that even if R0<1, there is still outbreak of disease. Meanwhile, we also investigate several control strategies with focus on their effects on epidemic inhibition. Furthermore, according to the numerical experiments, it is found that the bistability of the model not only has disease-free equilibrium and endemic equilibrium stable, but also has two endemic equilibrium stable. It should be emphasized that due to the effect of saturated treatment, the occurrence of a forward bifurcation at R0=1 does not guarantee that there is only one stable endemic equilibrium. In this case, the initial infection density is low enough to ensure the disease to reach another low endemic stable state.

A scenario modelling analysis to anticipate the impact of COVID-19 vaccination in adolescents and children on disease outcomes in the Netherlands, summer 2021.

BackgroundSince the roll-out of COVID-19 vaccines in late 2020 and throughout 2021, European governments have relied on mathematical modelling to inform policy decisions about COVID-19 vaccination.AimWe present a scenario-based modelling analysis in the Netherlands during summer 2021, to inform whether to extend vaccination to adolescents (12-17-year-olds) and children (5-11-year-olds).MethodsWe developed a deterministic, age-structured susceptible-exposed-infectious-recovered (SEIR) model and compared modelled incidences of infections, hospital and intensive care admissions, and deaths per 100,000 people across vaccination scenarios, before the emergence of the Omicron variant.ResultsOur model projections showed that, on average, upon the release of all non-pharmaceutical control measures on 1 November 2021, a large COVID-19 wave may occur in winter 2021/22, followed by a smaller, second wave in spring 2022, regardless of the vaccination scenario. The model projected reductions in infections/severe disease outcomes when vaccination was extended to adolescents and further reductions when vaccination was extended to all people over 5 years-old. When examining projected disease outcomes by age group, individuals benefitting most from extending vaccination were adolescents and children themselves. We also observed reductions in disease outcomes in older age groups, particularly of parent age (30-49 years), when children and adolescents were vaccinated, suggesting some prevention of onward transmission from younger to older age groups.ConclusionsWhile our scenarios could not anticipate the emergence/consequences of SARS-CoV-2 Omicron variant, we illustrate how our approach can assist decision making. This could be useful when considering to provide booster doses or intervening against future infection waves.

Analysis of Vector-host SEIR-SEI Dengue Epidemiological Model

Approximately worldwide 50 nations are still infected with the deadly dengue virus. This mosquito-borne illness spreads rapidly. Epidemiological models can provide fundamental recommendations for public health professionals, allowing them to analyze variables impacting disease prevention and control efforts. In this paper, we present a host-vector mathematical model that depicts the Dengue virus transmission dynamics utilizing a susceptible-exposed-infected-recovered (SEIR) model for the human interacting with a susceptible-exposed-infected (SEI) model for the mosquito. Using the Next Generation Technique, the basic reproduction number of the model is calculated. The local stability shows that if R0&lt;1 the system is asymptotically stable and the disease dies out, otherwise unstable. The Lyapunov function is also used to evaluate the global stability of disease-free and endemic equilibrium points. To analyze the effect of the crucial aspects of the disease's transmission and to validate the analytical findings, numerical simulations of a variety of compartments have been constructed using MATLAB. The sensitivity analysis of the epidemic model is performed to establish the relative significance of the model parameters to disease transmission.

NUMERICAL SIMULATION OF CORONAVIRUS DISEASE EPIDEMIC BASED ON ESTABLISHED SUSCEPTIBLE-EXPOSED-INFECTIOUS-RECOVERED-UNDETECTABLE-SUSCEPTIBLE MODEL

Coronavirus (COVID-19) is the virus which has killed so many people in the world. The spread of COVID-19 within a region in South East Asia has been modelled using a compartment model called SEIR (Susceptible, Exposed, Infected, Recovered). Actual number of sick people needing treatments, or the number active case data was used to obtain realistic values of the model parameter such as the reproduction number (R0), incubation, and recovery periods. It is shown that at the beginning of the pandemic where most people were still not aware, the R0 was very high as seen by the steep increase of people got infected and admitted to the hospitals. Few weeks after the lockdown of the region was in place and people were obeying the regulation and observing safe distancing, the R0 values dropped significantly and converged to a steady value of about 3. Using the obtained model parameters, fitted on a daily basis, the maximum number of active cases converged to a certain value of about 2500 cases. It is expected that in the early June 2020 that the number of active cases will drop to a significantly low level. We Implement SEIR model to enumerate the infected Population and the number of casualties of this pandemic. Numerical Simulations was carried out to set off the analytical results in investigating the effect of the implementation of Isolation and social distancing as a function of time.

Bayesian Inference for COVID-19 Transmission Dynamics in India Using a Modified SEIR Model

We propose a modified population-based susceptible-exposed-infectious-recovered (SEIR) compartmental model for a retrospective study of the COVID-19 transmission dynamics in India during the first wave. We extend the conventional SEIR methodology to account for the complexities of COVID-19 infection, its multiple symptoms, and transmission pathways. In particular, we consider a time-dependent transmission rate to account for governmental controls (e.g., national lockdown) and individual behavioral factors (e.g., social distancing, mask-wearing, personal hygiene, and self-quarantine). An essential feature of COVID-19 that is different from other infections is the significant contribution of asymptomatic and pre-symptomatic cases to the transmission cycle. A Bayesian method is used to calibrate the proposed SEIR model using publicly available data (daily new tested positive, death, and recovery cases) from several Indian states. The uncertainty of the parameters is naturally expressed as the posterior probability distribution. The calibrated model is used to estimate undetected cases and study different initial intervention policies, screening rates, and public behavior factors, that can potentially strike a balance between disease control and the humanitarian crisis caused by a sudden strict lockdown.

Modified susceptible–exposed–infectious–recovered model for assessing the effectiveness of non-pharmaceutical interventions during the COVID-19 pandemic in Seoul

Susceptible–exposed–infectious–recovered (SEIR) models were applied to assess the effectiveness of non-pharmaceutical interventions (NPIs) and to study the dynamic behavior of the COVID-19 pandemic. Recently, SEIR models have evolved to address the change of human mobility by some NPIs for predicting the new confirmed cases. However, the models have serious limitations when applied to Seoul. Seoul has two representative quarantine policies, i.e. social distancing and the ban on gatherings. Effects of the two policies need to be reflected in different functional forms in the model because changes in human mobility do not fully reflect the ban on gatherings. Thus we propose a modified SEIR model to assess the effectiveness of social distancing, ban on gatherings and vaccination strategies. The application of the modified SEIR model was illustrated by comparing the model output with real data.

Impact of the national hepatitis B immunization program in China: a modeling study

BackgroundElimination of hepatitis B virus (HBV) is a striking challenge for countries with high or moderate disease burden. Therefore, using China as a practical case to share experiences for similar countries may accelerate the achievement of the WHO 2030 target of 90% reduction in HBV-related incidence. We aim to evaluate the impact of national HBV immunization strategies in China; and the feasibility to achieve WHO 2030 targets under different scenarios.MethodsWe constructed an expanded Susceptible-Exposed-Infectious-Recovered (SEIR) model and decision tree-Markov model to estimate the epidemic of HBV in China, assess the feasibility of 2030 Elimination Goals through the projections and conduct the economic analysis. Least square method was used to calibrate the expanded SEIR model by yearly data of laboratory-confirmed HBV cases from 1990 to 2018. Two models were separately used to evaluate the impact and cost-effectiveness of HBV vaccine by comparing prevalence of chronic HBV infections, quality-adjusted life-years (QALYs), incremental cost effectiveness ratio and benefit–cost ratio (BCR) under various intervention options, providing a basis for exploring new containment strategies.ResultsBetween 1990 and 2020, the number of chronic HBV infections decreased by 33.9%. The current status quo would lead to 55.73 million infections (3.95% prevalence) in 2030, compared to 90.63 million (6.42% prevalence) of the “Without the NIP” scenario (NIP: National Immunization Program), 114.78 million (8.13% prevalence) without any interventions. The prevention of mother to child transmission (PMTCT) strategy showed a net benefit as 12,283.50 dollars per person, with BCR as 12.66, which is higher than that of universal vaccination at 9.49. Compared with no screening and no vaccination, the PMTCT strategy could save 7726.03 dollars for each QALY increase.ConclusionsOur findings proved the HBV vaccination has demonstrated a substantial positive impact on controlling the epidemic of HBV in terms of effectiveness and economy after about 30 years of implementation of the national hepatitis B immunization program which also provided containment experience for high or medium burden countries. As for China, the next step should focus on exploring strategies to improve diagnosis and treatment coverage to reduce the burden of HBV-related deaths and ultimately eliminate HBV.

Actuarial Modeling of COVID-19 Insurance

In this article, we provide an actuarial model expected to be able to help financial arrangements to cover losses due to the outbreak of coronavirus disease (COVID-19). We construct the dynamical models of premium and benefit based on generalized SEIR (Susceptible-Exposed-Infected-Recovered). Based on its dynamical model, we formulate the premium and the premium reserves on hospitalization and death benefits of the COVID-19 insurance.

Analysis of Covid-19 Using A Modified SEIR Model To Understand The Cases Registered in Singapore, Spain, And Venezuela

This work proposes a modification of a compartmental-type model based on the Susceptible-Exposed-Infected-Recovered (SEIR) scheme to describe the dynamics of contagion by Covid-19 in any part of the world, including also the numerical and analytical calculation of the mantissa and the resolution of a partial differential equation system. As an example, the different incidents that occurred in Singapore, Spain and Venezuela are analyzed to demonstrate the usefulness of the methodology developed in this work that can be seamlessly extended to other regions.

Modified SEIR and machine learning prediction of the trend of the epidemic of COVID-19 in Jordan under lockdowns impact

&lt;span&gt;Susceptible exposed infectious recovered (SEIR) is a fitting model for coronavirus disease (COVID-19) spread prediction. Hence, to examine the effect of different levels of social distancing on the spreading of the disease, a variable was introduced in the SEIR equations system used in this work. We also used an artificial intelligence approach using a machine learning (ML) method known as deep neural network. This modified SEIR model was applied on the available initial spread data until June 25&lt;sup&gt;th&lt;/sup&gt;, 2021 for the Hashemite Kingdom of Jordan. Without lockdown in Jordan, the analysis demonstrates potential infection to roughly 3.1 million people during the peak of spread approximately 3 months, starting from the date of lockdown (March 21&lt;sup&gt;st&lt;/sup&gt;). Conversely, the present partial lockdowns strategy by the Kingdom was expected to reduce the predicted number of infections to 0.5 million in 9 months period. The analysis also demonstrates the ability of stricter lockdowns to effectively flatten the graph curve of COVID-19 in Jordan. Our modified SEIR and deep neural network (DNN) model were efficient in the prediction of COVID-19 epidemic sizes and peaks. The measures taken to control the epidemic by the government decreased the size of the COVID-19 epidemic.&lt;/span&gt;

Modeling the impact of mitigation policies in a pandemic: A system dynamics approach

In the absence of effective and adequate vaccines, healthcare decision-makers must rely on non-pharmaceutical interventions (NPIs), such as lockdown, testing, hospital capacity building, and increasing the number of medical staff to control the outbreak of an infectious disease like COVID-19. This manuscript presents a System Dynamics (SD) model to analyze the healthcare system performance under various NPIs during a pandemic. The proposed model, which extends the commonly-used Susceptible-Exposed-Infectious-Recovered (SEIR) model, comprises four sub-models: outbreak, hospital performance, medicine supply, and staff functionality. These sub-models work in harmony to stimulate the impact of NPIs on the disease outbreak pattern and the healthcare system's response to demand surge. The proposed model considers the uncertainty about the nature of the disease, the public's behavior, medicine availability, and medical staff efficiency. The proposed model was applied for the ex-ante evaluation of candidate NPIs adoptable against the COVID-19 outbreak in Iran. Consistent with the reported statistics, the results show that the peak demand can significantly exceed the healthcare system's initial capacity if no action is taken. If simultaneously implemented, lockdown and testing can considerably delay the peak of infections, reduce its magnitude, dampen the hospital demand, and decrease mortality. The proposed model is unique as it determines the extent to which system components (e.g., community, healthcare system, and medicine supply chain) impact the observed outcomes (e.g., morbidity and mortality rates). Its structure is generic and flexible, which facilitates the extension and application of the model to evaluate candidate mitigation policies in various geographical contexts.

Análisis de modelos tipo SEIR utilizados en los inicios de la pandemia COVID-19 reportados en revistas de alto impacto

Introduction The Susceptible-Exposed-Infected-Recovered (SEIR) mathematical-epidemiological model has been exhaustively used since de beggining of the COVID-19 pandemic. These models intended to predict hospital burden and evaluate health measures to contain its spread. In this sense, flaws have been evidenced in the predictions of the first published models. It is considered necessary to evaluate the differences in the approach and verification of the models. Objectives We carried out a systematic review of the articles published in journals indexed in the Web of Science, of the first quartile and with an impact factor greater than two, that met the selection and inclusion criteria following the PRISMA-ScR standards. We included a total of 32 articles, which were evaluated according to demographic characteristics such as the month of receipt and publication, the country of origin of the information, the subject matter of the journal, and the characteristics of the modeling such as the presence of additional compartments, graphical analysis, conceptual model approach, interpretation of the basic reproductive number, and estimation of parameters. Methods Articles published in medical and health journals were predominant from February to July 2020. These articles most frequently used data from China and mostly focused on SEIR or full quarantine compartment models. The articles published in journals in mathematics were predominant from August to December 2020. Models used data from different world regions, considering a greater diversity of compartments such as asymptomatic patients or partial or complete quarantine. Results The articles analyzed mostly use SEIR-type models expanded with additional compartments. There are discrepancies in the breadth and methodological quality of the articles published according to the journal’s subject matter. The unification of quality criteria for describing the models in any journal is recommended.

State estimation of the time–space propagation of COVID-19 using a distributed parameter observer based on a SEIR-type model

The real-time prediction and estimation of the spread of diseases, such as COVID-19 is of paramount importance as evidenced by the recent pandemic. This work is concerned with the distributed parameter estimation of the time–space propagation of such diseases using a diffusion–reaction epidemiological model of the susceptible–exposed–infected–recovered (SEIR) type. State estimation is based on continuous measurements of the number of infections and deaths per unit of time and of the host spatial domain. The observer design method is based on positive definite matrices to parameterize a class of Lyapunov functionals, in order to stabilize the estimation error dynamics. Thus, the stability conditions can be expressed as a set of matrix inequality constraints which can be solved numerically using sum of squares (SOS) and standard semi-definite programming (SDP) tools. The observer performance is analyzed based on a simplified case study corresponding to the situation in France in March 2020 and shows promising results.

Exploring Dynamic Pandemic Containment Strategies Using Multi-Objective Optimization [Research Frontier

The SARS-CoV-2 pandemic demonstrates the vulnerability of societies in a globalized world. As pathogens spread at exponential rates, rapid development of appropriate medical treatments and distribution of vaccinations are major challenges. Under these circumstances, authorities employ non-pharmaceutical interventions (NPIs) against the spread, which can impact the economy strongly. Hence, there is a need for strategies that help minimize infection without sacrificing the economy’s wellbeing. This study explores the inherent trade-off characteristics of optimal control strategies by utilizing the well-known SEIR (susceptible, exposed, infectious, recovered) pandemic model with an integrated economic compartment. The health economy dilemma (HED) qualifies as a multi-objective optimization (MOO) problem and the goal is to find strategies which are optimal regarding concurrent infections, economic growth, and required intensity of employed interventions. The major contribution of this paper is to propose a new methodology for containment strategy exploration using MOO. The experiments show that the resulting solutions can contribute towards solving the HED by supporting the identification of optimal strategies. Specific characteristics of pandemics are highlighted in this novel tri-objective optimization approach.

Coronavirus Epidemic Spreading Prediction combining random walk with susceptible–exposed–infected–recovered–deceased (SEIRD) model

Since the breakout of COVID-19 pandemic in December 2019, effective modelling of the spreading of the virus has become an essential reference for the epidemic controlling. In a bid to solve the problem of Epidemic prediction, susceptible-exposed-infected-recovered (SEIR) model are widely applied. However, this model seems lack the ability to handle random events which may occur during the spreading of the pandemic and the ability to simulate the pandemic spreading between different subdivided regions. Therefore, we propose an early version of susceptible–exposed–infected–recovered–deceased (SEIRD) model that combines the classic compartmental concepts of SEIRD and the random walk methodology to forecast COVID-19 in real time. Specifically, this study will focus on improvement of the exposed–infected part of SEIRD model. First, the exposed–infected section of SEIRD model will be applied to each subdivided regions separated. Then, instead of entering infected–recovered part directly, the infected of each district will be selected and sent to linked districts by random walk system to mimic the commuting and irregular trips between regions. Eventually, after the re-distribution of infected patients, the model will enter the infected–recovered section. This argued model adopt the SEIRD model to forecasting of virus spreading between small regions and taking irregular moving of citizens into consideration via random walk system, thus provide an effective reference for countries which aim to respond to the post-epidemic era.

Model-Based Evaluation of Transmissibility and Intervention Measures for a COVID-19 Outbreak in Xiamen City, China.

BackgroundIn September 2021, there was an outbreak of coronavirus disease 2019 (COVID-19) in Xiamen, China. Various non-pharmacological interventions (NPIs) and pharmacological interventions (PIs) have been implemented to prevent and control the spread of the disease. This study aimed to evaluate the effectiveness of various interventions and to identify priorities for the implementation of prevention and control measures.MethodsThe data of patients with COVID-19 were collected from 8 to 30 September 2021. A Susceptible-Exposed-Infectious-Recovered (SEIR) dynamics model was developed to fit the data and simulate the effectiveness of interventions (medical treatment, isolation, social distancing, masking, and vaccination) under different scenarios. The effective reproductive number (Reff) was used to assess the transmissibility and transmission risk.ResultsA total of 236 cases of COVID-19 were reported in Xiamen. The epidemic curve was divided into three phases (Reff = 6.8, 1.5, and 0). Notably, the cumulative number of cases was reduced by 99.67% due to the preventive and control measures implemented by the local government. In the effective containment stage, the number of cases could be reduced to 115 by intensifying the implementation of interventions. The total number of cases (TN) could be reduced by 29.66–95.34% when patients voluntarily visit fever clinics. When only two or three of these measures are implemented, the simulated TN may be greater than the actual number. As four measures were taken simultaneously, the TN may be <100, which is 57.63% less than the actual number. The simultaneous implementation of five interventions could rapidly control the transmission and reduce the number of cases to fewer than 25.ConclusionWith the joint efforts of the government and the public, the outbreak was controlled quickly and effectively. Authorities could promptly cut the transmission chain and control the spread of the disease when patients with fever voluntarily went to the hospital. The ultimate effect of controlling the outbreak through only one intervention was not obvious. The combined community control and mask wearing, along with other interventions, could lead to rapid control of the outbreak and ultimately lower the total number of cases. More importantly, this would mitigate the impact of the outbreak on society and socioeconomics.

Predicting COVID-19 Infected Individuals in a Defined Population from Wastewater RNA Data.

Wastewater surveillance of SARS-CoV-2 RNA has become an important tool for tracking the presence of the virus and serving as an early indicator for the onset of rapid transmission. Nevertheless, wastewater data are still not commonly used to predict the number of infected individuals in a sewershed. The main objective of this study was to calibrate a susceptible-exposed-infectious-recovered (SEIR) model using RNA copy rates in sewage (i.e., gene copies per liter times flow rate) and the number of SARS-CoV-2 saliva-test-positive infected individuals in a university student population that was subject to repeated weekly testing during the Spring 2021 semester. A strong correlation was observed between the RNA copy rates and the number of infected individuals. The parameter in the SEIR model that had the largest impact on calibration was the maximum shedding rate, resulting in a mean value of 7.72 log10 genome copies per gram of feces. Regressing the saliva-test-positive infected individuals on predictions from the SEIR model based on the RNA copy rates yielded a slope of 0.87 (SE = 0.11), which is statistically consistent with a 1:1 relationship between the two. These findings demonstrate that wastewater surveillance of SARS-CoV-2 can be used to estimate the number of infected individuals in a sewershed.